I would not just order the LY battery. This depends on your manufacturing year. The LY battery has wires soldered onto it, but the old model does not have wires soldered onto it because there are contact points on the battery holder (like an old cell phone battery). Just open your mouse to be sure. Old model uses the L-L11 battery.

One tip: for the old model you don’t need to unscrew/remove the battery holder. Just take the battery out.